Zone of darkness surrounding view camera in eevee render preview
Okay, I just figured it out. I'm using a sun-lamp casting rays in a certain direction, but I also have three large objects in the distance that don't have materials set up and seem to be casting shadows.

If I hide them from view, the zone of darkness goes away.

This blend file is originally from blender internal, and I've been setting up the now blank materials in the scene to similar versions of the originals in eevee. The three distant objects are meant to represent features of a night sky; stars, the moon, the moon's glare. That's why they're there.